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On the Almost Sure Central Limit Theorem for a Class of Z d -Actions

Author

Listed:
  • Mikhail Gordin

    (V. A. Steklov Mathematical Institute at St Petersburg)

  • Michel Weber

    (Université Louis-Pasteur)

Abstract

As an extension of earlier papers on stationary sequences, a concept of weak dependence for strictly stationary random fields is introduced in terms of so-called homoclinic transformations. Under assumptions made within the framework of this concept a form of the almost sure central limit theorem (ASCLT) is established for random fields arising from a class of algebraic Z d -actions on compact abelian groups. As an auxillary result, the central limit theorem is proved via Ch. Stein's method. The next stage of the proof includes some estimates which are specific for ASCLT. Both steps are based on making use of homoclinic transformations.

Suggested Citation

  • Mikhail Gordin & Michel Weber, 2002. "On the Almost Sure Central Limit Theorem for a Class of Z d -Actions," Journal of Theoretical Probability, Springer, vol. 15(2), pages 477-501, April.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:2:d:10.1023_a:1015014927939
    DOI: 10.1023/A:1015014927939
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    References listed on IDEAS

    as
    1. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
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